Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
 
import java.util.*;
import java.lang.*;
import java.io.*;
 
@SuppressWarnings("unchecked")
public class Main implements Runnable {

  static BufferedReader in;
  static PrintWriter out;
 
  public static void main(String[] args) {
      new Thread(null, new Main(), "whatever", 1<<29).start();
  }
 
  public void run() {
    in = new BufferedReader(new InputStreamReader(System.in));
    out = new PrintWriter(System.out, false);
 
    try
    {
      // in = new BufferedReader(new FileReader("A-large (1).in"));
      // out = new PrintWriter("output.txt");

      int t,x1,n,m,i,j;
      String str;
      String[] token;

      str=in.readLine().trim();
      token=str.split(" ");
      n=Integer.parseInt(token[0]);

      m=(int)Math.ceil(((double)n+1.0)/2);

      out.println(m);

      int cnt=0;

      for(j=1;j<m;j++) {
        if(cnt<n) {
          out.println(1+" "+j);
          cnt++;
        }
      }

      for(i=1;i<=m;i++) {
        if(cnt<n) {
          out.println(i+" "+j);
          cnt++;
        }
      }

      out.flush();
      out.close();
    }
    catch(Exception e) {
      e.printStackTrace();
    }
  }
}